The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (4, 1) is a point on the curve?

Question

irishboy123 · Answer

dy/dx = ??

build and solve.....

anonymous · Answer

I'm not sure how to begin

irishboy123 · Answer

dy/dx = x / y

separate + solve with boundary condition (4, 1) .....

anonymous · Answer

How do you do the boundary condition?

irishboy123 · Answer

solve the differential equation first, and then use 4,1 to find the integration constant....

anonymous · Answer

would it be x+y=15

irishboy123 · Answer

if x + y = 15, 
then y = -x + 15 
so dy/dx = -1

it cannot be that, then.

do you know how to solve the diff equation?